Multiple integral representations for some families of hypergeometric and other polynomials
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TLDR
Each of the integral representations, which are derived in this paper, may be viewed also as a linearization relationship for the product of two different members of the associated family of hypergeometric and other polynomials.About:
This article is published in Mathematical and Computer Modelling.The article was published on 2011-09-01 and is currently open access. It has received 9 citations till now. The article focuses on the topics: Generalized hypergeometric function & Barnes integral.read more
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Integral representations for the Lagrange polynomials, Shively’s pseudo-Laguerre polynomials, and the generalized Bessel polynomials
TL;DR: In this article, the Lagrange polynomials, Shively pseudo-Laguerre (SLL), and generalized Bessel (GBS) were investigated and the corresponding integral representations were derived.
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Statistical approximation properties of high order operators constructed with the Chan–Chyan–Srivastava polynomials
Esra Erkuş-Duman,Oktay Duman +1 more
TL;DR: By including high order derivatives of functions being approximated, a general family of the linear positive operators constructed by means of the Chan–Chyan–Srivastava multivariable polynomials is introduced and a Korovkin-type approximation result is obtained, which is more applicable than the classical case.
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Integral representations for the generalized Bedient polynomials and the generalized Cesàro polynomials
TL;DR: Each of the integral representations, which are derived in this paper, may be viewed also as a linearization relationship for the product of two different members of the associated family of hypergeometric polynomials.
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Two-parameter Srivastava polynomials and several series identities
Cem Kaanoglu,Mehmet Ali Özarslan +1 more
TL;DR: In this paper, two-parameter Srivastava polynomials are introduced, where they reduce to Laguerre, Jacobi, Bessel and Lagrange.
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Linearization of the products of the Carlitz-Srivastava polynomials of the first and second kinds via their integral representations
TL;DR: Upon suitable specialization of the main results presented in this paper, the corresponding integral representations are deduced for such familiar classes of multivariable hypergeometric polynomials as (for example) the Lauricella polynomsials F"D^(^r^) in r variables and the Appell polynomes F"1 in two variables.
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A course of modern analysis; an introduction to the general theory of infinite processes and of analytic functions; with an account of the principal transcendental functions
TL;DR: The theory of Riemann integration as mentioned in this paper is a generalization of the theory of complex numbers, and it can be expressed as follows: 1. Complex numbers 2. The theory of convergence 3. Continuous functions and uniform convergence 4. The fundamental properties of analytic functions 5. The expansion of functions in infinite series 6.
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Statistical approximation of certain positive linear operators constructed by means of the Chan-Chyan-Srivastava polynomials
TL;DR: By obtaining some Korovkin type approximation results in statistical sense for certain positive linear operators constructed by means of the Chan-Chyan-Srivastava multivariable polynomials, it is shown that the approximation method is stronger than the corresponding classical aspects in the approximation theory settings.